DSCI353-353m-453: Class 9b Layers Loss Optimizers, Classify Movie Revs

Profs: R. H. French, L. S. Bruckman, P. Leu, K. Davis, S. Cirlos

Class Readings, Assignments, Syllabus Topics

Reading, Lab Exercises, SemProjects

• Readings:
  • For today: DLwR4, DL12,13
  • For next class: DLwR5 and Hinton Imagenet
    • Krizhevsky Hinton - 2012 - ImageNet Classification with Deep Convolutional NN-paper.pdf
    • Krizhevsky Hinton - 2012 - ImageNet Classification with Deep Convolutional NN-talk.pdf
• Laboratory Exercises:
  • LE5: Given out today
  • LE5: Due Saturday April 1st
• Office Hours: (Class Canvas Calendar for Zoom Link)
  • Wednesdays @ 4:00 PM to 5:00 PM
    
  • Saturdays @ 3:00 PM to 4:00 PM
  • Office Hours are on Zoom, and recorded
• Semester Projects
  • Office Hours for SemProjs: Mondays at 4pm on Zoom
  • DSCI 453 Students Biweekly Updates Due
    • Update # is Due ** **
  • DSCI 453 Students
    • Next Report Out #2 is Due Friday March 24th
  • All DSCI 353/353M/453, E1453/2453 Students:
    • Peer Grading of Report Out #2 is Due Friday March 31st
  • Exams
    • Final: Thursday May 4th, 2023, 12:00PM - 3:00PM, Nord 356 or remote

Syllabus

IT Fundamentals: Applied Data Science with R, Syllabus

---

Some Notes on TensorFlow2 and Markov

• For TF2 we say TF2 or DLwR in the class notes title
• You want to use OnDemand
• Its best to use Markov (KDE) desktop
  • And its Dolphin File Manager
  • And its Konsole terminal
• Its easiest to launch R/Rstudio, Python3/Spyder using desktop icons
• nvidia-smi will confirm that you have a GPU

This notebook contains the code samples

• found in Chapter 3, Section 5 of Deep Learning with R.
• Note that the original text features far more content,
  • in particular further explanations and figures:
• in this notebook, you will only find source code and related comments.

If you compile to pdf,

• the .nb.html file contains the training details

---

Keras/TensorFlow concepts

Anatomy of a neural network

• Training a neural network revolves around the following objects:

  • Layers, which are combined into a network (or model )
  • The input data and corresponding targets/responses
  • The loss function, which defines the feedback signal used for learning
  • The optimizer, which determines how learning proceeds

You can visualize their interaction as illustrated in figure 3.1:

• the network,
  • composed of layers that are chained together,
  • maps the input data to predictions.
• the loss function then
  • compares these predictions to the targets,
  • producing a loss value: a measure of
  • how well the network’s predictions match what was expected.
• The optimizer uses this loss value
  • to update the network’s weights.

Figure 3.1 The network, layers, loss function, and optimizer

Layers: the building blocks of deep learning

• The fundamental data structure in neural networks is the layer

A layer is a data-processing module that

• takes as input one or more tensors and
• that outputs one or more tensors.

Some layers are stateless, but more frequently layers have a state:

• the layer’s weights,
  • one or several tensors learned with stochastic gradient descent,
• which together contain the network’s knowledge.

Different layers are appropriate for

• different tensor formats and
• different types of data processing.

For instance,

• simple vector data,
  • stored in 2D tensors of shape (samples, features),
  • is often processed by densely connected layers,
    • also called fully connected or dense layers
    • (the layer_dense function in Keras).
• Sequence data,
  • stored in 3D tensors of shape (samples, timesteps, features),
  • is typically processed by recurrent layers
    • such as layer_lstm.
• Image data,
  • stored in 4D tensors,
  • is usually processed by 2D convolution layers (layer_conv_2d).

You can think of layers as the LEGO bricks of deep learning,

• a metaphor that is made explicit by frameworks like Keras.

Building deep-learning models in Keras is done by

• clipping together compatible layers
• to form useful data-transformation pipelines.

The notion of layer compatibility here refers specifically to the fact that

• every layer will only accept input tensors of a certain shape and
• will return output tensors of a certain shape.

Models: networks of layers

• A deep-learning model is a directed, acyclic graph of layers.

  • The most common instance is a linear stack of layers,
    • mapping a single input to a single output.
  • But as you move forward,
    • you’ll be exposed to a much broader variety of network topologies.

Some common ones include the following:

• Two-branch networks
• Multihead networks
• Inception blocks

The topology of a network defines a hypothesis space.

• We define machine learning as
  • “searching for useful representations of some input data,
  • within a predefined space of possibilities,
  • using guidance from a feedback signal.”
• By choosing a network topology,
  • you constrain your space of possibilities (the hypothesis space)
  • to a specific series of tensor operations,
    • mapping input data to output data.
• What you’ll then be searching for is
  • a good set of values for the weight tensors
    • involved in these tensor operations.

Picking the right network architecture

• is more an art than a science;
  • and although there are some best practices and principles you can rely on,
• only practice can help you become a proper neural-network architect.

The next few chapters will both teach you

• explicit principles for building neural networks and help you
• develop intuition as to
  • what works or doesn’t work for specific problems.

Loss functions and optimizers: keys to configuring the learning process

• Once the network architecture is defined, you still have to choose two more things:

  • Loss function (objective function)
  • The quantity that will be minimized during training.
  • It represents a measure of success for the task at hand.
  • Optimizer
    • Determines how the network will be updated
      • based on the loss function.
    • It implements a specific variant of stochastic gradient descent (SGD).

A neural network that has multiple outputs

• may have multiple loss functions (one per output).
• But the gradient-descent process
  • must be based on a single scalar loss value;
• So, for multiloss networks,
  • all losses are combined (via averaging)
  • into a single scalar quantity.

Choosing the right objective (or loss) function

• for the right problem is extremely important:
• your network will take any shortcut it can,
  • to minimize the loss;
• so if the objective doesn’t fully correlate
  • with success for the task at hand,
• your network will end up doing things you may not have wanted.

Imagine a stupid, omnipotent AI

• trained via SGD, with this poorly chosen objective function:
  • “maximizing the average well-being of all humans alive.”
• To make its job easier, this AI might choose to
  • kill all humans except a few
  • and focus on the well-being of the remaining ones
  • because average well-being isn’t affected by how many humans are left.
• That might not be what you intended!
  • Just remember that all neural networks you build
  • will be just as ruthless in lowering their loss function
    • so choose the objective wisely,
    • or you’ll have to face unintended side effects.

Fortunately, when it comes to common problems

• such as classification, regression, and sequence prediction,
• there are simple guidelines you can follow to choose the correct loss.

For instance, the Loss Functions you’ll use are

• binary crossentropy for a two-class classification problem,
• categorical crossentropy for a many-class classification problem,
• mean-squared error for a regression problem,
• connectionist temporal classification (CTC) for a sequence-learning problem,
• and so on.

Only when you’re working on truly new research problems

• will you have to develop your own objective functions.

Going forward we’ll detail explicitly

• which loss functions to choose
• for a wide range of common tasks.

Introduction to Keras

• Keras is a deep-learning framework that

  • provides a convenient way to define and train
  • almost any kind of deep-learning model.

Keras was initially developed for researchers,

• with the aim of enabling fast experimentation.

Keras has the following key features:

• It allows the same code to run seamlessly on CPU or GPU.
• It has a user-friendly API that makes it easy
  • to quickly prototype deep-learning models.
• It has built-in support for
  • convolutional networks (for computer vision),
  • recurrent networks (for sequence processing),
  • and any combination of both.
• It supports arbitrary network architectures:
  • multi-input or multi-output models,
  • layer sharing,
  • model sharing, and so on.

This means Keras is appropriate for building essentially any deep-learning model,

• from a generative adversarial network
• to a neural Turing machine.

Keras and its R interface

• are distributed under the permissive MIT license,
• which means they can be freely used in commercial projects.

The Keras R package is compatible with R versions 3.2 and higher.

The documentation for the R interface

• is available at [https://keras.rstudio.com](https://keras.rstudio.com_.

The main Keras project website

• can be found at https://keras.io.

Keras has well over 250,000 users (as of 2018),

• ranging from academic researchers and engineers
  • at both startups and large companies
  • to graduate students and hobbyists.

Keras is used at Google, Netflix, Uber, CERN, Yelp, Square, and others

• working on a wide range of problems.

Keras is also a popular framework on Kaggle,

• the machine-learning competition website,
• where almost every recent deep-learning competition
• has been won using Keras models (see figure 3.2).

Figure 3.2 Google web search interest for different deep-learning frameworks over time

Keras, TensorFlow, Theano, and CNTK

• Keras is a model-level library,

  • providing high-level building blocks
  • for developing deep-learning models.

It doesn’t handle low-level operations

• such as tensor manipulation and differentiation.
• Instead, it relies on
  • a specialized, well-optimized tensor library to do so,
  • serving as the backend engine of Keras.
• Rather than choosing a single tensor library and
  • tying the implementation of Keras to that library,
  • Keras handles the problem in a modular way (see figure 3.3);
• Thus, several different backend engines
  • can be plugged seamlessly into Keras.

Currently, the three existing backend implementations are

• the TensorFlow2 backend,
• the Theano backend, and
  • “On 28 September 2017, Pascal Lamblin posted a message from Yoshua Bengio, Head of MILA: major development would cease after the 1.0 release due to competing offerings by strong industrial players.”
• the Microsoft Cognitive Toolkit (CNTK) backend.
  • “Today’s 2.7 release will be the last main release of CNTK.”

In the future, it’s likely that Keras will be extended

• to work with even more deep-learning execution engines.

One popular Deep Learning Framework is PyTorch

• Which uses dynamic computation graphs
• And is not supported by Keras.

You can see mulitple deep learning frameworks here.

Figure 3.3 The deep-learning software and hardware stack

TensorFlow, CNTK (deprecated), and Theano (deprecated)

• are some of the primary platforms for deep learning today.
• Theano
  • was developed by the MILA lab at Université de Montréal,
  • And stopeed development in 2017
• CNTK
  • was developed by Microsoft.
  • and stopped development in 2018

TensorFlow2

• is developed by Google
  • Who released TensorFlow2 in Sept. 2019
• TensorFlow: Large-Scale Machine Learning on Heterogeneous Distributed Systems
  • In 3-readings/2-articles

Starting in 2011, Google Brain built DistBelief

• as a proprietary machine learning system
  • based on deep learning neural networks.
• Its use grew rapidly across diverse Alphabet companies
  • in both research and commercial applications.
• Google assigned multiple computer scientists, including Jeff Dean,
  • to simplify and refactor the codebase of DistBelief
    • into a faster, more robust application-grade library,
  • which became TensorFlow.
• In 2009, the team, led by Geoffrey Hinton,
  • had implemented generalized backpropagation and other improvements
• which allowed generation of neural networks
  • with substantially higher accuracy,
  • for instance a 25% reduction in errors in speech recognition.

Google has also developed the Tensor Processing Unit

• Which focuses on expanding beyond GPU 2D matrix operations
  • To volumetric 3D operations
• “Tensor” units are now implemented by Nvidia in their GPUs

Any piece of code that you write with Keras

• can be run with any of these backends
  • without having to change anything in the code:
• you can seamlessly switch between the two during development,
  • which often proves useful
• for instance, if one of these backends proves to be faster for a specific task.

We recommend using the TensorFlow backend

• as the default for most of your deep-learning needs,
• because it’s the most widely adopted, scalable, and production ready.

Via TensorFlow (or Theano, or CNTK), Keras is able to run seamlessly

• on both CPUs and GPUs.

When running on CPU, TensorFlow is itself

• wrapping a low-level library for tensor operations,
• called Eigen.

On GPU, TensorFlow

• wraps a library of well-optimized deep-learning operations
• called the NVIDIA CUDA Deep Neural Network library.

Developing with Keras

• You’ve already seen one example of a Keras model:

  • the MNIST example.

The typical Keras workflow looks just like that example:

• Define your training data:
  • input tensors and target tensors.
• Define a network of layers (or model )
  • that maps your inputs to your targets.
• Configure the learning process by choosing
  • a loss function,
  • an optimizer, and
  • some metrics to monitor.
• Iterate on your training data
  • by calling the fit() method of your model.

There are two ways to define a model:

• using the keras_model_sequential() function
  • (only for linear stacks of layers,
    • which is the most common network architecture by far)
• or the functional API
  • (for directed acyclic graphs of layers,
    • which let you build completely arbitrary architectures).

As a refresher, here’s a two-layer model

• defined using keras_model_sequential
  • (note that we’re passing
    • the expected shape of the input data to the first layer):

model <- keras_model_sequential() %>% layer_dense(units = 32, input_shape = c(784)) %>% layer_dense(units = 10, activation = "softmax")

And here’s the same model defined using the functional API:

input_tensor <- layer_input(shape = c(784)) output_tensor <- input_tensor %>% layer_dense(units = 32, activation = "relu") %>% layer_dense(units = 10, activation = "softmax") model <- keras_model(inputs = input_tensor, outputs = output_tensor)

With the functional API,

• you’re manipulating the data tensors
  • that the model processes and
• applying layers to this tensor
  • as if they were functions.

Once your model architecture is defined,

• it doesn’t matter whether you used keras_model_sequential
  • or the functional API.
• All of the following steps are the same.

The learning process is configured in the compilation step,

• where you specify
  • the optimizer and
  • loss function(s)
  • that the model should use,
• as well as the metrics
  • you want to monitor during training.

Here’s an example with a single loss function,

• which is by far the most common case:

model %>% compile( optimizer = optimizer_rmsprop(lr = 0.0001), loss = "mse", metrics = c("accuracy") )

Finally, the learning process

• consists of passing arrays of input data
  • (and the corresponding target data)
• to the model via the fit() method,
  • similar to what you’d do with other machine-learning libraries:

model %>% fit(input_tensor, target_tensor, batch_size = 128, epochs = 10)

Going forward we’ll build a solid intuition

• about what type of network architectures
  • work for different kinds of problems,
• how to pick the right learning configuration, and
  • how to tweak a model
• until it gives the results you want to see.

Two-class classification, or binary classification,

• may be the most widely applied kind of machine learning problem.

In this example, we will learn to classify movie reviews

• into “positive” reviews and “negative” reviews,
  
• just based on the text content of the reviews.

Lets confirm we are setup with TF2, GPU

Lets check that we have TF2 and a GPU setup

tensorflow::as_tensor(1)

## tf.Tensor(1.0, shape=(), dtype=float64)

And below, you’ll see active R code blocks

• These are for TF2 v2.11, which we are running
• The below, inactive code block
  • Is for TF2 v2.6
• For comparison of changes in TF2 version
  • https://www.tensorflow.org/versions

The IMDB dataset

• We’ll be working with “IMDB dataset”,

  • a set of 50,000 highly-polarized reviews from the Internet Movie Database.
    • They are split into 25,000 reviews for training
    • and 25,000 reviews for testing,
  • each set consisting in 50% negative and 50% positive reviews.

Why do we have these two separate training and test sets?

• You should never test a machine learning model
  • on the same data that you used to train it!
• Just because a model performs well on its training data
  • doesn’t mean that it will perform well on data it has never seen,
• and what you actually care about is your model’s performance on new data
  • (since you already know the labels of your training data
  • obviously you don’t need your model to predict those).

For instance, it is possible that your model

• could end up merely memorizing a mapping
  • between your training samples and their targets
• which would be completely useless
  • for the task of predicting targets for data never seen before.
• We will go over this point in much more detail in the next chapter.

Just like the MNIST dataset,

• the IMDB dataset comes packaged with Keras.

It has already been preprocessed:

• the reviews (sequences of words) have been turned into sequences of integers,
• where each integer stands for a specific word in a dictionary.

The following code will load the dataset

• (when you run it for the first time,
  • about 80MB of data will be downloaded to your machine):
• But I have already saved the dataset into the ./data folder

library(keras)

imdb <- dataset_imdb(num_words = 10000)
c(c(train_data, train_labels), c(test_data, test_labels)) %<-% imdb

# ```{r}
library(keras)

# imdb <- dataset_imdb(num_words = 10000) # here keras reads it from AWS storage
imdb <-
  readRDS("./data/imdb.rds") # or load copy stored in data subfolder

c(c(train_data, train_labels), c(test_data, test_labels)) %<-% imdb

The argument num_words = 10000

• means that we will only keep the top 10,000
  • most frequently occurring words in the training data.
• Rare words will be discarded.
• This allows us to work with vector data of manageable size.

The variables train_data and test_data are lists of reviews,

• each review being a list of word indices
  • (encoding a sequence of words).
• train_labels and test_labels are lists of 0s and 1s,
  • where 0 stands for “negative”
  • and 1 stands for “positive”:

str(train_data)

## List of 25000
##  $ : int [1:218] 1 14 22 16 43 530 973 1622 1385 65 ...
##  $ : int [1:189] 1 194 1153 194 8255 78 228 5 6 1463 ...
##  $ : int [1:141] 1 14 47 8 30 31 7 4 249 108 ...
##  $ : int [1:550] 1 4 2 2 33 2804 4 2040 432 111 ...
##  $ : int [1:147] 1 249 1323 7 61 113 10 10 13 1637 ...
##  $ : int [1:43] 1 778 128 74 12 630 163 15 4 1766 ...
##  $ : int [1:123] 1 6740 365 1234 5 1156 354 11 14 5327 ...
##  $ : int [1:562] 1 4 2 716 4 65 7 4 689 4367 ...
##  $ : int [1:233] 1 43 188 46 5 566 264 51 6 530 ...
##  $ : int [1:130] 1 14 20 47 111 439 3445 19 12 15 ...
##  $ : int [1:450] 1 785 189 438 47 110 142 7 6 7475 ...
##  $ : int [1:99] 1 54 13 1610 14 20 13 69 55 364 ...
##  $ : int [1:117] 1 13 119 954 189 1554 13 92 459 48 ...
##  $ : int [1:238] 1 259 37 100 169 1653 1107 11 14 418 ...
##  $ : int [1:109] 1 503 20 33 118 481 302 26 184 52 ...
##  $ : int [1:129] 1 6 964 437 7 58 43 1402 11 6 ...
##  $ : int [1:163] 1 7092 1662 11 4 1749 9 4 2165 4 ...
##  $ : int [1:752] 1 33 4 5673 7 4 2 194 2 3089 ...
##  $ : int [1:212] 1 13 28 64 69 4 8742 7 319 14 ...
##  $ : int [1:177] 1 3432 26 9 6 1220 731 939 44 6 ...
##  $ : int [1:129] 1 617 11 3875 17 2 14 966 78 20 ...
##  $ : int [1:140] 1 466 49 2036 204 2442 40 4 6724 732 ...
##  $ : int [1:256] 1 13 784 886 857 15 135 142 40 2 ...
##  $ : int [1:888] 1 4 712 19 2 2 2 963 2 26 ...
##  $ : int [1:93] 1 4 204 7610 20 16 93 11 9075 19 ...
##  $ : int [1:142] 1 14 9 6 55 641 2854 212 44 6 ...
##  $ : int [1:220] 1 4 288 310 3202 7 241 672 4 2 ...
##  $ : int [1:193] 1 75 69 8 140 8 35 2 38 75 ...
##  $ : int [1:171] 1 4679 2784 1482 11 450 7 134 364 352 ...
##  $ : int [1:221] 1 13 28 332 4 274 6 378 7 211 ...
##  $ : int [1:174] 1 13 1059 14 33 6 2181 2824 32 13 ...
##  $ : int [1:647] 1 6 565 255 5964 875 103 196 167 2 ...
##  $ : int [1:233] 1 4 86 390 1241 520 6 52 1384 51 ...
##  $ : int [1:162] 1 13 92 124 51 12 9 13 169 38 ...
##  $ : int [1:597] 1 111 28 3431 15 2 475 455 4127 9 ...
##  $ : int [1:234] 1 1255 1223 5547 1265 2390 1747 8 4 268 ...
##  $ : int [1:51] 1 806 13 43 161 169 4 875 551 17 ...
##  $ : int [1:336] 1 23 3333 7449 7505 4 254 157 2 7 ...
##  $ : int [1:139] 1 17 19 111 85 1719 1181 3135 201 14 ...
##  $ : int [1:231] 1 14 38 446 1034 9 394 13 435 8 ...
##  $ : int [1:704] 1 14 16 4 840 5582 20 5 4 236 ...
##  $ : int [1:142] 1 14 22 16 23 522 33 314 54 13 ...
##  $ : int [1:861] 1 1710 14 733 1367 1028 81 24 332 48 ...
##  $ : int [1:132] 1 4 229 18 14 248 1844 1422 9 38 ...
##  $ : int [1:122] 1 3420 9 34 230 61 514 7 32 7 ...
##  $ : int [1:570] 1 11 14 4419 3073 14 9061 50 26 1093 ...
##  $ : int [1:55] 1 568 65 9 4689 31 7 4 118 495 ...
##  $ : int [1:214] 1 806 21 13 80 2372 199 4 114 347 ...
##  $ : int [1:103] 1 54 7850 5397 8633 7455 9 2090 2 23 ...
##  $ : int [1:186] 1 13 244 1713 1681 8 97 134 243 7 ...
##  $ : int [1:113] 1 13 165 219 14 20 33 6 750 17 ...
##  $ : int [1:169] 1 159 13 296 14 22 13 332 6 733 ...
##  $ : int [1:469] 1 14 364 1242 2460 2 47 43 77 7548 ...
##  $ : int [1:138] 1 1400 168 855 19 12 50 26 76 128 ...
##  $ : int [1:302] 1 101 20 11 63 7564 2 46 1421 6 ...
##  $ : int [1:766] 1 5011 892 711 12 2774 38 2428 145 11 ...
##  $ : int [1:351] 1 1318 13 191 264 146 4 86 5 64 ...
##  $ : int [1:146] 1 13 974 13 69 8 702 930 143 14 ...
##  $ : int [1:59] 1 13 296 4 20 11 6 4435 5 13 ...
##  $ : int [1:206] 1 209 888 14 22 47 8 30 31 7 ...
##  $ : int [1:107] 1 13 219 14 33 4 2 22 1413 12 ...
##  $ : int [1:152] 1 591 92 851 42 60 104 44 2644 14 ...
##  $ : int [1:186] 1 13 258 14 20 8 30 6 87 326 ...
##  $ : int [1:431] 1 4 2019 9 149 16 35 221 22 585 ...
##  $ : int [1:147] 1 146 242 31 7 4 1126 2406 2266 451 ...
##  $ : int [1:684] 1 1810 8 516 7732 93 6 227 7 6 ...
##  $ : int [1:383] 1 1028 11 86 8213 14 1327 1210 1124 5205 ...
##  $ : int [1:324] 1 2 8810 322 7398 5 68 1667 476 2 ...
##  $ : int [1:252] 1 13 286 1017 76 5 8 30 1202 13 ...
##  $ : int [1:263] 1 48 335 6 337 7 22 1359 5 104 ...
##  $ : int [1:787] 1 6 1380 6733 3453 54 49 432 7 5682 ...
##  $ : int [1:211] 1 14 20 218 290 4 22 12 16 3551 ...
##  $ : int [1:314] 1 49 24 38 2 1028 1404 10 10 138 ...
##  $ : int [1:118] 1 480 302 18 6 20 7 14 58 6 ...
##  $ : int [1:390] 1 670 5304 1616 97 6 20 40 14 21 ...
##  $ : int [1:132] 1 1756 5663 9 2990 2 133 177 17 6 ...
##  $ : int [1:710] 1 1065 2474 7 3508 2 645 113 17 6 ...
##  $ : int [1:306] 1 17 210 14 9 35 6213 431 7 4 ...
##  $ : int [1:167] 1 2500 1040 4 327 1208 44 14 215 28 ...
##  $ : int [1:115] 1 11 4 402 3469 111 7 178 37 69 ...
##  $ : int [1:95] 1 435 8 67 14 17 72 5 61 761 ...
##  $ : int [1:158] 1 31 7 61 118 369 839 14 20 120 ...
##  $ : int [1:156] 1 66 371 2 2 373 21 284 2 2567 ...
##  $ : int [1:82] 1 4 1126 282 13 69 8 67 14 20 ...
##  $ : int [1:502] 1 14 22 7930 236 314 33 2 5510 750 ...
##  $ : int [1:314] 1 13 144 1260 138 13 520 14 418 7 ...
##  $ : int [1:190] 1 13 92 400 140 46 7 61 96 8 ...
##  $ : int [1:174] 1 61 795 203 30 6 227 7 6 1361 ...
##  $ : int [1:60] 1 18 6 20 19 6 114 40 14 13 ...
##  $ : int [1:145] 1 13 219 14 22 5236 145 137 780 23 ...
##  $ : int [1:214] 1 11 192 5192 2 125 2139 1253 7 2 ...
##  $ : int [1:659] 1 541 5156 517 19 4 4791 7 2408 827 ...
##  $ : int [1:408] 1 474 66 66 473 8 67 14 20 5 ...
##  $ : int [1:515] 1 7931 4 425 410 2568 4 876 7 4 ...
##  $ : int [1:461] 1 121 81 13 895 13 473 8 358 14 ...
##  $ : int [1:202] 1 13 66 215 28 1059 6 275 22 39 ...
##  $ : int [1:238] 1 827 2 2 10 10 1251 8598 300 2 ...
##  $ : int [1:170] 1 24 15 76 183 593 11 14 20 21 ...
##  $ : int [1:107] 1 14 20 9 389 10 10 13 16 2 ...
##   [list output truncated]

str(train_data[[1]])

str(train_labels)

##  int [1:25000] 1 0 0 1 0 0 1 0 1 0 ...

train_labels[[1]]

Since we restricted ourselves to the top 10,000 most frequent words,

• no word index will exceed 10,000:

max(sapply(train_data, max))

## [1] 9999

max(sapply(train_data, max))

For kicks,

• here’s how you can quickly decode
• one of these reviews back to English words:

word_index <- dataset_imdb_word_index()

reverse_word_index <- names(word_index)
names(reverse_word_index) <- as.character(word_index)

decoded_words <- train_data[[1]] %>%
  sapply(function(i) {
    if (i > 3)
      reverse_word_index[[as.character(i - 3)]]
    else
      "?"
  })
decoded_review <- paste0(decoded_words, collapse = " ")

# word_index is a dictionary mapping words to an integer index
word_index <- dataset_imdb_word_index()

# We reverse it, mapping integer indices to words
reverse_word_index <- names(word_index)
names(reverse_word_index) <- word_index

# We decode the review; note that our indices were offset by 3
# because 0, 1 and 2 are reserved indices for "padding", "start of sequence", and "unknown".
decoded_review <- sapply(train_data[[1]], function(index) {
  word <-
    if (index >= 3)
      reverse_word_index[[as.character(index - 3)]]
  if (!is.null(word))
    word
  else
    "?"
})

decoded_review

## [1] "? this film was just brilliant casting location scenery story direction everyone's really suited the part they played and you could just imagine being there robert ? is an amazing actor and now the same being director ? father came from the same scottish island as myself so i loved the fact there was a real connection with this film the witty remarks throughout the film were great it was just brilliant so much that i bought the film as soon as it was released for ? and would recommend it to everyone to watch and the fly fishing was amazing really cried at the end it was so sad and you know what they say if you cry at a film it must have been good and this definitely was also ? to the two little boy's that played the ? of norman and paul they were just brilliant children are often left out of the ? list i think because the stars that play them all grown up are such a big profile for the whole film but these children are amazing and should be praised for what they have done don't you think the whole story was so lovely because it was true and was someone's life after all that was shared with us all"

cat(decoded_review)

Preparing the data

• You can’t feed lists of integers into a neural network.

  • You have to turn your lists into tensors.

There are two ways to do that:

• Pad your lists so that they all have the same length,
  • turn them into an integer tensor of shape (samples, word_indices),
  • and then use as the first layer in your network
    • a layer capable of handling such integer tensors
    • (the “embedding” layer, which we’ll cover in detail later in the book).
• One-hot-encode your lists to turn them into vectors of 0s and 1s.
  • This would mean, for instance, turning the sequence [3, 5]
    • into a 10,000-dimensional vector that would be all zeros
    • except for indices 3 and 5, which would be ones.
  • Then you could use as the first layer in your network a dense layer,
    • capable of handling floating-point vector data.

Let’s go with the latter solution

• and vectorize the data,
• which you’ll do manually for maximum clarity.

vectorize_sequences <- function(sequences, dimension = 10000) {
  # Create an all-zero matrix of shape (len(sequences), dimension)
  results <- array(0, dim = c(length(sequences), dimension))
  for (i in seq_along(sequences)) {
    # Sets specific indices of results[i] to 1s
    sequence <- sequences[[i]]
    for (j in sequence)
      results[i, j] <- 1
  }
  results
}

# Our vectorized training data
x_train <- vectorize_sequences(train_data)

# Our vectorized test data
x_test <- vectorize_sequences(test_data)

vectorize_sequences <- function(sequences, dimension = 10000) {
  # Create an all-zero matrix of shape (len(sequences), dimension)
  results <- matrix(0, nrow = length(sequences), ncol = dimension)
  for (i in 1:length(sequences))
    # Sets specific indices of results[i] to 1s
    results[i, sequences[[i]]] <- 1
  results
}

# Our vectorized training data
x_train <- vectorize_sequences(train_data)

# Our vectorized test data
x_test <- vectorize_sequences(test_data)

Here’s what our samples look like now:

str(x_train)

##  num [1:25000, 1:10000] 1 1 1 1 1 1 1 1 1 1 ...

str(x_train[1,])

We should also vectorize our labels,

• which is straightforward:

# Our vectorized labels
y_train <- as.numeric(train_labels)
y_test <- as.numeric(test_labels)

# Our vectorized labels
y_train <- as.numeric(train_labels)
y_test <- as.numeric(test_labels)

Now our data is ready to be fed into a neural network.

Building our network

• Activation Functions

  • Used in the Nodes/Neurons of a layer
    • Can be of many types, depending of the purpose of the layer
  • relu is a Rectified Linear Unit
  • Sigmoid or Logistic is another
  • the simple Step function Softmax
    • is often used in output layers

Our input data is vectors, and the labels are scalars (1s and 0s):

• this is the easiest setup you’ll ever encounter.
• A type of network that performs well on such a problem
  • is a simple stack of fully connected (“dense”) layers
  • with relu activations:
  • layer_dense(units = 16, activation = "relu").

The argument being passed to each dense layer (16)

• is the number of hidden units of the layer.
• A hidden unit is a dimension in the representation space of the layer.
• You may remember from chapter 2 that each such dense layer
  • with a relu activation
  • implements the following chain of tensor operations:
  • output = relu(dot(W, input) + b)

Having 16 hidden units means that the weight matrix W

• will have shape (input_dimension, 16),
• i.e. the dot product with W will project the input data
  • onto a 16-dimensional representation space
  • (and then we would add the bias vector b and apply the relu operation). You can intuitively understand the dimensionality of your representation space
• as “how much freedom you are allowing the network to have
  • when learning internal representations”.
• Having more hidden units (a higher-dimensional representation space)
  • allows your network to learn more complex representations,
  • but it makes your network more computationally expensive
  • and may lead to learning unwanted patterns
• (patterns that will improve performance
  • on the training data but not on the test data).

There are two key architecture decisions to be made

• about such a stack of dense layers:
  • How many layers to use.
  • How many “hidden units” to chose for each layer.

In the next chapter, you will learn formal principles

• to guide you in making these choices.

For the time being, you will have to trust us

• with the following architecture choice:
  • two intermediate layers with 16 hidden units each,
  • and a third layer which will output the scalar prediction
  • regarding the sentiment of the current review.
• The intermediate layers will use relu as their “activation function”,
• and the final layer will use a sigmoid activation
  • so as to output a probability
  • (a score between 0 and 1,
  • indicating how likely the sample is to have the target “1”,
  • i.e. how likely the review is to be positive).
• A relu (rectified linear unit)
  • is a function meant to zero-out negative values,
• while a sigmoid “squashes” arbitrary values into the [0, 1] interval,
  • thus outputting something that can be interpreted as a probability.

Here’s what our network looks like:

3-layer network

And here’s the Keras implementation,

• very similar to the MNIST example you saw previously:

model <- keras_model_sequential() %>%
  layer_dense(16, activation = "relu") %>%
  layer_dense(16, activation = "relu") %>%
  layer_dense(1, activation = "sigmoid")

library(keras)

model <- keras_model_sequential() %>%
  layer_dense(units = 16,
              activation = "relu",
              input_shape = c(10000)) %>%
  layer_dense(units = 16, activation = "relu") %>%
  layer_dense(units = 1, activation = "sigmoid")

Lastly, we need to pick a loss function and an optimizer.

• Since we are facing a binary classification problem

  • and the output of our network is a probability
    • (we end our network with a single-unit layer with a sigmoid activation),
  • is it best to use the binary_crossentropy loss.
  • It isn’t the only viable choice:
    • you could use, for instance, mean_squared_error.
  • But crossentropy is usually the best choice
    • when you are dealing with models that output probabilities.
  • Crossentropy is a quantity from the field of Information Theory,
    • that measures the “distance” between probability distributions,
  • or in our case, between the ground-truth distribution and our predictions.

Here’s the step where we configure our model

• with the rmsprop optimizer
• and the binary_crossentropy loss function.

Note that we will also monitor accuracy during training.

model %>% compile(optimizer = "rmsprop",
                  loss = "binary_crossentropy",
                  metrics = "accuracy")

model %>% compile(optimizer = "rmsprop",
                  loss = "binary_crossentropy",
                  metrics = c("accuracy"))

You’re passing your optimizer, loss function, and metrics as strings,

• which is possible because rmsprop, binary_crossentropy, and accuracy
  • are packaged as part of Keras.
• Sometimes you may want to
  • configure the parameters of your optimizer
  • or pass a custom loss function or metric function.
• The former can be done by
  • passing an optimizer instance as the optimizer argument:

Here is an example of reducing the learning rate lr

model %>% compile(
  optimizer = optimizer_rmsprop(lr = 0.001),
  loss = "binary_crossentropy",
  metrics = c("accuracy")
) 

The latter can be done by

• passing function objects
  • as the loss or metrics arguments:

model %>% compile(optimizer = optimizer_rmsprop(lr = 0.001),
                  loss = loss_binary_crossentropy,
                  metrics = metric_binary_accuracy) 

Validating our approach

• In order to monitor during training

  • the accuracy of the model on data that it has never seen before,
  • we will create a “validation set”
    • by setting apart 10,000 samples
    • from the original training data:

x_val <- x_train[seq(10000),]
partial_x_train <- x_train[-seq(10000),]
y_val <- y_train[seq(10000)]
partial_y_train <- y_train[-seq(10000)]

val_indices <- 1:10000

x_val <- x_train[val_indices, ]
partial_x_train <- x_train[-val_indices, ]

y_val <- y_train[val_indices]
partial_y_train <- y_train[-val_indices]

# ```{r, echo=TRUE, results='hide'}
model %>% compile(optimizer = "rmsprop",
                  loss = "binary_crossentropy",
                  metrics = c("accuracy"))

We will now train our model for 20 epochs

• (20 iterations over all samples in the x_train and y_train tensors),
  • in mini-batches of 512 samples.
• At this same time we will monitor loss and accuracy
  • on the 10,000 samples that we set apart.
• This is done by passing the validation data
  • as the validation_data argument:

history <- model %>% fit(
  partial_x_train,
  partial_y_train,
  epochs = 20,
  batch_size = 512,
  validation_data = list(x_val, y_val)
)

history <- model %>% fit(
  partial_x_train,
  partial_y_train,
  epochs = 20,
  batch_size = 512,
  validation_data = list(x_val, y_val)
)

On GPU, this will take less than two seconds per epoch

• training is over in 20 seconds.
• At the end of every epoch,
  • there is a slight pause as the model computes its loss and accuracy
  • on the 10,000 samples of the validation data.

Note that the call to fit() returns a history object.

• Let’s take a look at it:

str(history$metrics)

## List of 4
##  $ loss        : num [1:20] 0.564 0.356 0.268 0.216 0.182 ...
##  $ accuracy    : num [1:20] 0.75 0.89 0.916 0.93 0.94 ...
##  $ val_loss    : num [1:20] 0.435 0.338 0.3 0.293 0.282 ...
##  $ val_accuracy: num [1:20] 0.858 0.876 0.884 0.882 0.886 ...

str(history)

The history object includes

• various parameters used to fit the model (history$params)
• as well as data for each of the metrics being monitored (history$metrics).

The history object

• has a plot() method that enables us
• to visualize the training and validation metrics by epoch:

plot(history)

plot(history)

history_df <- as.data.frame(history)
str(history_df)

## 'data.frame':    80 obs. of  4 variables:
##  $ epoch : int  1 2 3 4 5 6 7 8 9 10 ...
##  $ value : num  0.564 0.356 0.268 0.216 0.182 ...
##  $ metric: Factor w/ 2 levels "loss","accuracy": 1 1 1 1 1 1 1 1 1 1 ...
##  $ data  : Factor w/ 2 levels "training","validation": 1 1 1 1 1 1 1 1 1 1 ...

The accuracy is plotted on the bottom panel

• and the loss on the top panel.

Note that your own results may vary slightly

• due to a different random initialization of your network.

The dots are the training loss and accuracy,

• while the solid lines are the validation loss and accuracy.

Note that your own results may vary slightly

• due to a different random initialization of your network.

As you can see,

• the training loss decreases with every epoch,
• and the training accuracy increases with every epoch.

That’s what you would expect when running a gradient-descent optimization

• the quantity you’re trying to minimize should be less with every iteration.
• But that isn’t the case for the validation loss and accuracy:
  • they seem to peak at the fourth epoch.
• This is an example of what we warned against earlier:
  • a model that performs better on the training data
  • isn’t necessarily a model that will do better
  • on data it has never seen before.
• In precise terms, what you’re seeing is overfitting:
  • after the second epoch,
  • you’re over-optimizing on the training data,
• and you end up learning representations
  • that are specific to the training data = and don’t generalize to data outside of the training set.

In this case, to prevent overfitting,

• you could stop training after three epochs.
• In general, you can use a range of techniques
  • to mitigate overfitting, which we’ll cover in chapter 4.

Let’s train a new network from scratch

• for four epochs
• and then evaluate it on the test data.

model <- keras_model_sequential() %>%
  layer_dense(16, activation = "relu") %>%
  layer_dense(16, activation = "relu") %>%
  layer_dense(1, activation = "sigmoid")

model %>% compile(optimizer = "rmsprop",
                  loss = "binary_crossentropy",
                  metrics = "accuracy")

model %>% fit(x_train, y_train, epochs = 4, batch_size = 512)

results <- model %>% evaluate(x_test, y_test)

# ```{r, echo=TRUE, results='hide'}

model <- keras_model_sequential() %>%
  layer_dense(units = 16,
              activation = "relu",
              input_shape = c(10000)) %>%
  layer_dense(units = 16, activation = "relu") %>%
  layer_dense(units = 1, activation = "sigmoid")

model %>% compile(optimizer = "rmsprop",
                  loss = "binary_crossentropy",
                  metrics = c("accuracy"))

model %>% fit(x_train, y_train, epochs = 4, batch_size = 512)
results <- model %>% evaluate(x_test, y_test)

library(tidyverse)

## ── Attaching core tidyverse packages ──────────────────────── tidyverse 2.0.0 ──
## ✔ dplyr     1.1.0     ✔ readr     2.1.4
## ✔ forcats   1.0.0     ✔ stringr   1.5.0
## ✔ ggplot2   3.4.1     ✔ tibble    3.1.8
## ✔ lubridate 1.9.2     ✔ tidyr     1.3.0
## ✔ purrr     1.0.1     
## ── Conflicts ────────────────────────────────────────── tidyverse_conflicts() ──
## ✖ dplyr::filter() masks stats::filter()
## ✖ dplyr::lag()    masks stats::lag()
## ℹ Use the ]8;;http://conflicted.r-lib.org/conflicted package]8;; to force all conflicts to become errors

glimpse(results)

##  Named num [1:2] 0.297 0.88
##  - attr(*, "names")= chr [1:2] "loss" "accuracy"

results

Our fairly naive approach achieves an accuracy of 88%.

• With state-of-the-art approaches,

  • one should be able to get close to 95%.

Using a trained network to generate predictions on new data

After having trained a network,

• you’ll want to use it in a practical setting.
• You can generate the likelihood of reviews being positive
  • by using the predict method:

##                  [,1]
##     [1,] 1.809323e-01
##     [2,] 9.995760e-01
##     [3,] 5.644663e-01
##     [4,] 7.213696e-01
##     [5,] 9.194620e-01
##     [6,] 6.935150e-01
##     [7,] 9.976543e-01
##     [8,] 7.234948e-03
##     [9,] 9.577290e-01
##    [10,] 9.708132e-01
##    [11,] 8.362126e-01
##    [12,] 6.386790e-03
##    [13,] 1.489181e-04
##    [14,] 1.815337e-02
##    [15,] 9.927796e-01
##    [16,] 1.730158e-04
##    [17,] 9.071934e-01
##    [18,] 4.735232e-01
##    [19,] 4.328170e-03
##    [20,] 4.784987e-02
##    [21,] 9.950227e-01
##    [22,] 9.919990e-01
##    [23,] 2.480482e-01
##    [24,] 9.167549e-01
##    [25,] 7.412857e-01
##    [26,] 9.200405e-01
##    [27,] 2.976402e-02
##    [28,] 9.044346e-01
##    [29,] 9.465023e-01
##    [30,] 2.464158e-04
##    [31,] 9.706364e-01
##    [32,] 1.398314e-01
##    [33,] 8.715113e-01
##    [34,] 5.860220e-06
##    [35,] 3.201670e-02
##    [36,] 1.004452e-02
##    [37,] 9.976768e-01
##    [38,] 9.292197e-01
##    [39,] 1.351627e-01
##    [40,] 8.702021e-03
##    [41,] 9.681451e-01
##    [42,] 9.973466e-01
##    [43,] 1.391261e-02
##    [44,] 8.738510e-01
##    [45,] 9.989918e-01
##    [46,] 9.346272e-01
##    [47,] 3.169743e-02
##    [48,] 7.066271e-04
##    [49,] 1.031139e-02
##    [50,] 2.579865e-01
##    [51,] 3.586534e-03
##    [52,] 2.287266e-01
##    [53,] 7.119795e-01
##    [54,] 8.712035e-01
##    [55,] 8.180949e-01
##    [56,] 1.252218e-01
##    [57,] 5.272564e-01
##    [58,] 7.468358e-01
##    [59,] 3.089978e-03
##    [60,] 5.150989e-01
##    [61,] 4.404311e-02
##    [62,] 9.598553e-02
##    [63,] 8.767567e-01
##    [64,] 2.096784e-02
##    [65,] 1.827111e-02
##    [66,] 9.980721e-01
##    [67,] 1.213066e-02
##    [68,] 9.582978e-01
##    [69,] 9.885002e-01
##    [70,] 9.398970e-01
##    [71,] 8.965307e-01
##    [72,] 9.865780e-01
##    [73,] 5.067729e-01
##    [74,] 2.249002e-02
##    [75,] 2.204237e-02
##    [76,] 1.566965e-01
##    [77,] 2.578089e-03
##    [78,] 8.847433e-01
##    [79,] 6.601347e-01
##    [80,] 6.861193e-02
##    [81,] 4.444609e-01
##    [82,] 1.718397e-01
##    [83,] 3.732988e-01
##    [84,] 6.856255e-01
##    [85,] 2.177953e-03
##    [86,] 1.406798e-03
##    [87,] 2.340028e-02
##    [88,] 8.392849e-01
##    [89,] 9.339944e-03
##    [90,] 6.785294e-01
##    [91,] 9.990683e-01
##    [92,] 4.857672e-01
##    [93,] 3.968510e-02
##    [94,] 9.945129e-01
##    [95,] 9.980665e-01
##    [96,] 8.129402e-02
##    [97,] 7.468572e-01
##    [98,] 9.747097e-01
##    [99,] 4.450744e-02
##   [100,] 5.905495e-03
##   [101,] 2.456990e-02
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##   [103,] 1.159520e-04
##   [104,] 2.015492e-02
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##   [107,] 1.843619e-02
##   [108,] 1.053376e-01
##   [109,] 7.776293e-01
##   [110,] 9.964370e-01
##   [111,] 9.996836e-01
##   [112,] 1.088510e-03
##   [113,] 7.170403e-01
##   [114,] 2.514736e-01
##   [115,] 4.222094e-02
##   [116,] 7.150003e-01
##   [117,] 7.513252e-01
##   [118,] 9.092721e-04
##   [119,] 7.531762e-01
##   [120,] 9.357364e-01
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##   [123,] 4.657017e-03
##   [124,] 9.820311e-01
##   [125,] 9.640484e-01
##   [126,] 7.660322e-01
##   [127,] 7.673048e-01
##   [128,] 1.306863e-02
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##   [130,] 5.176824e-03
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##   [132,] 2.904397e-02
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##   [139,] 9.363435e-04
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##   [141,] 7.041843e-01
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##   [143,] 9.618140e-01
##   [144,] 7.432850e-05
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##   [149,] 9.532307e-01
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##   [157,] 6.571940e-01
##   [158,] 6.893743e-01
##   [159,] 7.582055e-05
##   [160,] 7.753600e-02
##   [161,] 3.169566e-02
##   [162,] 5.482108e-02
##   [163,] 1.254499e-04
##   [164,] 1.149191e-03
##   [165,] 9.730701e-01
##   [166,] 1.907135e-03
##   [167,] 3.755822e-01
##   [168,] 3.931412e-01
##   [169,] 3.929486e-02
##   [170,] 1.024042e-03
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##   [177,] 1.925038e-01
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##   [179,] 1.303269e-02
##   [180,] 3.211652e-01
##   [181,] 1.206163e-03
##   [182,] 2.083421e-01
##   [183,] 2.944685e-03
##   [184,] 7.957228e-04
##   [185,] 8.774836e-01
##   [186,] 1.202555e-01
##   [187,] 3.069976e-05
##   [188,] 6.423677e-02
##   [189,] 9.904826e-01
##   [190,] 2.864188e-03
##   [191,] 5.195049e-01
##   [192,] 4.365724e-01
##   [193,] 6.515576e-02
##   [194,] 6.253177e-03
##   [195,] 5.939679e-02
##   [196,] 9.778400e-01
##   [197,] 7.763751e-01
##   [198,] 1.092788e-03
##   [199,] 1.454827e-02
##   [200,] 7.223861e-02
##   [201,] 9.667301e-01
##   [202,] 2.997223e-04
##   [203,] 4.230601e-02
##   [204,] 9.621647e-01
##   [205,] 8.574087e-03
##   [206,] 3.993372e-01
##   [207,] 8.735950e-01
##   [208,] 4.249405e-03
##   [209,] 9.832233e-06
##   [210,] 9.915915e-01
##   [211,] 7.247230e-01
##   [212,] 9.809872e-01
##   [213,] 9.353937e-01
##   [214,] 1.234602e-02
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##   [217,] 1.584352e-03
##   [218,] 7.233366e-04
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##   [220,] 3.953746e-02
##   [221,] 2.174541e-02
##   [222,] 9.282452e-01
##   [223,] 1.724616e-02
##   [224,] 5.986146e-01
##   [225,] 5.983247e-01
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## [24789,] 6.573298e-03
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## [24797,] 1.357750e-01
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## [24799,] 1.560921e-01
## [24800,] 2.005600e-03
## [24801,] 5.385218e-02
## [24802,] 4.161819e-03
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## [24804,] 9.860895e-01
## [24805,] 5.373286e-06
## [24806,] 5.521966e-01
## [24807,] 6.292091e-01
## [24808,] 1.791318e-02
## [24809,] 8.759705e-01
## [24810,] 2.021309e-02
## [24811,] 1.264515e-01
## [24812,] 6.165643e-03
## [24813,] 6.518010e-01
## [24814,] 5.639805e-02
## [24815,] 5.188947e-01
## [24816,] 9.626456e-01
## [24817,] 1.679293e-01
## [24818,] 9.906137e-01
## [24819,] 3.389786e-01
## [24820,] 2.812696e-02
## [24821,] 1.741720e-02
## [24822,] 9.390001e-01
## [24823,] 1.300966e-02
## [24824,] 1.231894e-02
## [24825,] 6.428911e-02
## [24826,] 8.809685e-01
## [24827,] 7.909036e-01
## [24828,] 5.836832e-02
## [24829,] 9.246130e-01
## [24830,] 2.102110e-03
## [24831,] 5.196188e-02
## [24832,] 9.020481e-02
## [24833,] 1.991838e-03
## [24834,] 9.925183e-01
## [24835,] 6.026426e-02
## [24836,] 9.989079e-01
## [24837,] 6.845502e-01
## [24838,] 4.905607e-01
## [24839,] 9.832087e-01
## [24840,] 9.900144e-01
## [24841,] 7.789637e-05
## [24842,] 8.450133e-02
## [24843,] 9.063631e-01
## [24844,] 3.670092e-02
## [24845,] 1.998778e-02
## [24846,] 8.629155e-01
## [24847,] 8.769152e-01
## [24848,] 1.277260e-01
## [24849,] 9.718027e-01
## [24850,] 9.718598e-01
## [24851,] 7.734422e-03
## [24852,] 1.216102e-02
## [24853,] 7.641162e-01
## [24854,] 4.675112e-03
## [24855,] 4.889610e-01
## [24856,] 6.248385e-01
## [24857,] 5.383789e-03
## [24858,] 2.675319e-01
## [24859,] 2.330573e-05
## [24860,] 9.296845e-01
## [24861,] 4.471177e-01
## [24862,] 8.755432e-01
## [24863,] 2.726047e-01
## [24864,] 4.574155e-03
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## [24866,] 1.951344e-02
## [24867,] 6.756607e-02
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## [24869,] 9.412595e-01
## [24870,] 7.719343e-01
## [24871,] 7.038699e-01
## [24872,] 8.919522e-02
## [24873,] 3.379346e-01
## [24874,] 5.591932e-01
## [24875,] 7.739745e-03
## [24876,] 9.994985e-01
## [24877,] 9.569312e-01
## [24878,] 8.726880e-02
## [24879,] 8.079720e-01
## [24880,] 1.737255e-01
## [24881,] 3.129116e-05
## [24882,] 1.182594e-03
## [24883,] 6.712236e-01
## [24884,] 4.761741e-02
## [24885,] 1.263323e-01
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## [24887,] 2.435417e-01
## [24888,] 1.131691e-02
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## [24890,] 1.478861e-01
## [24891,] 9.823903e-01
## [24892,] 6.510865e-01
## [24893,] 9.395406e-01
## [24894,] 7.526447e-01
## [24895,] 8.403794e-03
## [24896,] 8.151969e-01
## [24897,] 1.746117e-03
## [24898,] 2.412618e-04
## [24899,] 2.244237e-02
## [24900,] 9.355348e-01
## [24901,] 9.536199e-01
## [24902,] 1.627520e-01
## [24903,] 2.204280e-03
## [24904,] 2.712900e-03
## [24905,] 6.765408e-03
## [24906,] 9.993649e-01
## [24907,] 9.838021e-01
## [24908,] 1.164848e-03
## [24909,] 9.774272e-01
## [24910,] 1.539741e-01
## [24911,] 2.136132e-01
## [24912,] 7.221838e-05
## [24913,] 5.100614e-03
## [24914,] 3.384619e-03
## [24915,] 9.619740e-01
## [24916,] 2.633864e-02
## [24917,] 8.624977e-01
## [24918,] 6.356140e-02
## [24919,] 9.645644e-01
## [24920,] 8.817286e-01
## [24921,] 4.695052e-01
## [24922,] 3.372674e-02
## [24923,] 9.998477e-01
## [24924,] 6.261634e-02
## [24925,] 7.205223e-02
## [24926,] 1.380065e-02
## [24927,] 6.337003e-01
## [24928,] 6.172195e-02
## [24929,] 5.139667e-03
## [24930,] 3.453147e-01
## [24931,] 6.248859e-02
## [24932,] 9.808352e-01
## [24933,] 9.060351e-01
## [24934,] 6.590093e-03
## [24935,] 9.874194e-01
## [24936,] 9.859599e-01
## [24937,] 3.036077e-01
## [24938,] 3.147335e-02
## [24939,] 4.322355e-02
## [24940,] 9.660822e-01
## [24941,] 9.593841e-01
## [24942,] 9.178557e-01
## [24943,] 6.986324e-01
## [24944,] 4.669711e-02
## [24945,] 9.896827e-01
## [24946,] 2.755826e-03
## [24947,] 1.309591e-01
## [24948,] 3.828813e-03
## [24949,] 2.656065e-02
## [24950,] 1.732427e-01
## [24951,] 8.113167e-01
## [24952,] 8.724517e-07
## [24953,] 1.262761e-06
## [24954,] 7.182690e-01
## [24955,] 1.210095e-01
## [24956,] 9.999441e-01
## [24957,] 6.794735e-03
## [24958,] 1.760919e-01
## [24959,] 1.250728e-02
## [24960,] 7.475549e-02
## [24961,] 1.444033e-02
## [24962,] 9.228146e-01
## [24963,] 1.383160e-01
## [24964,] 4.136506e-02
## [24965,] 8.014644e-04
## [24966,] 9.961369e-03
## [24967,] 3.663588e-01
## [24968,] 9.460790e-01
## [24969,] 7.004834e-01
## [24970,] 6.017078e-01
## [24971,] 9.941562e-01
## [24972,] 6.928720e-03
## [24973,] 8.979579e-03
## [24974,] 9.614748e-01
## [24975,] 9.489493e-01
## [24976,] 4.653215e-01
## [24977,] 3.306066e-03
## [24978,] 9.751461e-01
## [24979,] 5.848497e-01
## [24980,] 3.631917e-01
## [24981,] 9.019862e-01
## [24982,] 9.766631e-01
## [24983,] 9.695361e-01
## [24984,] 3.587396e-03
## [24985,] 5.377835e-01
## [24986,] 2.998480e-01
## [24987,] 9.924567e-01
## [24988,] 1.068753e-03
## [24989,] 9.328419e-01
## [24990,] 4.176937e-01
## [24991,] 6.621515e-01
## [24992,] 4.278349e-04
## [24993,] 9.964071e-01
## [24994,] 3.808199e-01
## [24995,] 9.620006e-01
## [24996,] 9.972059e-01
## [24997,] 4.791435e-01
## [24998,] 8.716574e-02
## [24999,] 7.349376e-02
## [25000,] 4.632613e-01

model %>% predict(x_test[1:10, ])

As you can see, the network is very confident for some samples

• (0.99 or more, or 0.02 or less)
• but less confident for others.

Further experiments

• We were using 2 hidden layers.
  • Try to use 1 or 3 hidden layers
  • and see how it affects validation and test accuracy.
• Try to use layers with more hidden units or less hidden units:
  • 32 units, 64 units…
• Try to use the mse loss function
  • instead of binary_crossentropy.
• Try to use the tanh activation
  • (an activation that was popular in the early days of neural networks)
  • instead of relu.

These experiments will help convince you

• that the architecture choices we have made
  • are all fairly reasonable,
• although they can still be improved!

Conclusions

• Here’s what you should take away from this example:

  • You usually need to do quite a bit of preprocessing on your raw data
    • in order to be able to feed it
    • as tensors – into a neural network.
    • Sequences of words can be encoded as binary vectors,
    • but there are other encoding options, too.
  • Stacks of dense layers with relu activations
    • can solve a wide range of problems
    • (including sentiment classification),
    • and you’ll likely use them frequently.
  • In a binary classification problem (two output classes),
    • your network should end with a dense layer
    • with one unit and a sigmoid activation.
    • That is, the output of your network
    • should be a scalar between 0 and 1,
    • encoding a probability.
  • With such a scalar sigmoid output on a binary classification problem,
    • the loss function you should use is binary_crossentropy.
  • The rmsprop optimizer is generally a good enough choice,
    • whatever your problem.
    • That’s one less thing for you to worry about.
  • As they get better on their training data,
    • neural networks eventually start overfitting
    • and end up obtaining increasingly worse results
    • on data they’ve never seen before.
    • Be sure to always monitor performance
    • on data that is outside of the training set.

Links

[1] Francois Chollet, J. J. Allaire, Deep Learning with R, https://www.manning.com/books/deep-learning-with-r Manning Publications, 2018.